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By Thomas Ferraro

WASHINGTON, Jan 17 (Reuters) - U.S. President-elect Barack Obama's proposed Cabinet of top advisers seems headed toward swift U.S. Senate approval, with former presidential rival Hillary Clinton appearing a shoo-in for secretary of state.

Following a tradition in the treatment of incoming presidents, Obama's fellow Democrats along with Republicans have made Senate confirmation of his Cabinet a top priority.

Most of Obama's picks may be approved within days of the Illinois Democrat being sworn in as the 44th president at noon (1700 GMT) on Tuesday. A few are expected to be confirmed within hours of the inauguration.

Twelve of President Ronald Reagan's 14 Cabinet members were confirmed within two days of his first inauguration in 1981, while 13 of President Bill Clinton's 15 Cabinet members were confirmed within one day.

President George W. Bush's Cabinet took longer to seat, with seven winning confirmation the first day and the rest approved within 11 days, according to Senate Democrats.

Members of both parties agree Obama's proposed department heads need to be in place to help him hit the ground running as he confronts two wars, a deepening recession, an explosive Middle East and an estimated 46 million Americans without healthcare.

Hillary Clinton, a senator from New York since 2001 and wife of former President Bill Clinton, may be the first of Obama's nominees to be confirmed, likely a few hours after he takes office. Clinton, who was Obama's chief rival for the Democratic presidential nomination, had her nomination sent to the full Senate by a 16-1 vote of the Foreign Relations Committee.